Identifier
Values
0 => [1] => 1 => 0
1 => [1] => 1 => 0
00 => [2] => 10 => 1
01 => [1,1] => 11 => 0
10 => [1,1] => 11 => 0
11 => [2] => 10 => 1
000 => [3] => 100 => 2
001 => [2,1] => 101 => 1
010 => [1,1,1] => 111 => 0
011 => [1,2] => 110 => 2
100 => [1,2] => 110 => 2
101 => [1,1,1] => 111 => 0
110 => [2,1] => 101 => 1
111 => [3] => 100 => 2
0000 => [4] => 1000 => 3
0001 => [3,1] => 1001 => 2
0010 => [2,1,1] => 1011 => 1
0011 => [2,2] => 1010 => 1
0100 => [1,1,2] => 1110 => 3
0101 => [1,1,1,1] => 1111 => 0
0110 => [1,2,1] => 1101 => 2
0111 => [1,3] => 1100 => 3
1000 => [1,3] => 1100 => 3
1001 => [1,2,1] => 1101 => 2
1010 => [1,1,1,1] => 1111 => 0
1011 => [1,1,2] => 1110 => 3
1100 => [2,2] => 1010 => 1
1101 => [2,1,1] => 1011 => 1
1110 => [3,1] => 1001 => 2
1111 => [4] => 1000 => 3
00000 => [5] => 10000 => 4
00001 => [4,1] => 10001 => 3
00010 => [3,1,1] => 10011 => 2
00011 => [3,2] => 10010 => 3
00100 => [2,1,2] => 10110 => 3
00101 => [2,1,1,1] => 10111 => 1
00110 => [2,2,1] => 10101 => 2
00111 => [2,3] => 10100 => 4
01000 => [1,1,3] => 11100 => 4
01001 => [1,1,2,1] => 11101 => 3
01010 => [1,1,1,1,1] => 11111 => 0
01011 => [1,1,1,2] => 11110 => 4
01100 => [1,2,2] => 11010 => 4
01101 => [1,2,1,1] => 11011 => 2
01110 => [1,3,1] => 11001 => 3
01111 => [1,4] => 11000 => 4
10000 => [1,4] => 11000 => 4
10001 => [1,3,1] => 11001 => 3
10010 => [1,2,1,1] => 11011 => 2
10011 => [1,2,2] => 11010 => 4
10100 => [1,1,1,2] => 11110 => 4
10101 => [1,1,1,1,1] => 11111 => 0
10110 => [1,1,2,1] => 11101 => 3
10111 => [1,1,3] => 11100 => 4
11000 => [2,3] => 10100 => 4
11001 => [2,2,1] => 10101 => 2
11010 => [2,1,1,1] => 10111 => 1
11011 => [2,1,2] => 10110 => 3
11100 => [3,2] => 10010 => 3
11101 => [3,1,1] => 10011 => 2
11110 => [4,1] => 10001 => 3
11111 => [5] => 10000 => 4
000000 => [6] => 100000 => 5
000001 => [5,1] => 100001 => 4
000010 => [4,1,1] => 100011 => 3
000011 => [4,2] => 100010 => 4
000100 => [3,1,2] => 100110 => 3
000101 => [3,1,1,1] => 100111 => 2
000110 => [3,2,1] => 100101 => 3
000111 => [3,3] => 100100 => 2
001000 => [2,1,3] => 101100 => 4
001001 => [2,1,2,1] => 101101 => 1
001010 => [2,1,1,1,1] => 101111 => 1
001011 => [2,1,1,2] => 101110 => 3
001100 => [2,2,2] => 101010 => 1
001101 => [2,2,1,1] => 101011 => 2
001110 => [2,3,1] => 101001 => 4
001111 => [2,4] => 101000 => 5
010000 => [1,1,4] => 111000 => 5
010001 => [1,1,3,1] => 111001 => 4
010010 => [1,1,2,1,1] => 111011 => 3
010011 => [1,1,2,2] => 111010 => 5
010100 => [1,1,1,1,2] => 111110 => 5
010101 => [1,1,1,1,1,1] => 111111 => 0
010110 => [1,1,1,2,1] => 111101 => 4
010111 => [1,1,1,3] => 111100 => 5
011000 => [1,2,3] => 110100 => 5
011001 => [1,2,2,1] => 110101 => 4
011010 => [1,2,1,1,1] => 110111 => 2
011011 => [1,2,1,2] => 110110 => 2
011100 => [1,3,2] => 110010 => 5
011101 => [1,3,1,1] => 110011 => 3
011110 => [1,4,1] => 110001 => 4
011111 => [1,5] => 110000 => 5
100000 => [1,5] => 110000 => 5
100001 => [1,4,1] => 110001 => 4
100010 => [1,3,1,1] => 110011 => 3
100011 => [1,3,2] => 110010 => 5
100100 => [1,2,1,2] => 110110 => 2
100101 => [1,2,1,1,1] => 110111 => 2
100110 => [1,2,2,1] => 110101 => 4
>>> Load all 1022 entries. <<<
100111 => [1,2,3] => 110100 => 5
101000 => [1,1,1,3] => 111100 => 5
101001 => [1,1,1,2,1] => 111101 => 4
101010 => [1,1,1,1,1,1] => 111111 => 0
101011 => [1,1,1,1,2] => 111110 => 5
101100 => [1,1,2,2] => 111010 => 5
101101 => [1,1,2,1,1] => 111011 => 3
101110 => [1,1,3,1] => 111001 => 4
101111 => [1,1,4] => 111000 => 5
110000 => [2,4] => 101000 => 5
110001 => [2,3,1] => 101001 => 4
110010 => [2,2,1,1] => 101011 => 2
110011 => [2,2,2] => 101010 => 1
110100 => [2,1,1,2] => 101110 => 3
110101 => [2,1,1,1,1] => 101111 => 1
110110 => [2,1,2,1] => 101101 => 1
110111 => [2,1,3] => 101100 => 4
111000 => [3,3] => 100100 => 2
111001 => [3,2,1] => 100101 => 3
111010 => [3,1,1,1] => 100111 => 2
111011 => [3,1,2] => 100110 => 3
111100 => [4,2] => 100010 => 4
111101 => [4,1,1] => 100011 => 3
111110 => [5,1] => 100001 => 4
111111 => [6] => 100000 => 5
0000000 => [7] => 1000000 => 6
0000001 => [6,1] => 1000001 => 5
0000010 => [5,1,1] => 1000011 => 4
0000011 => [5,2] => 1000010 => 5
0000100 => [4,1,2] => 1000110 => 4
0000101 => [4,1,1,1] => 1000111 => 3
0000110 => [4,2,1] => 1000101 => 4
0000111 => [4,3] => 1000100 => 5
0001000 => [3,1,3] => 1001100 => 5
0001001 => [3,1,2,1] => 1001101 => 3
0001010 => [3,1,1,1,1] => 1001111 => 2
0001011 => [3,1,1,2] => 1001110 => 3
0001100 => [3,2,2] => 1001010 => 4
0001101 => [3,2,1,1] => 1001011 => 3
0001110 => [3,3,1] => 1001001 => 4
0001111 => [3,4] => 1001000 => 6
0010000 => [2,1,4] => 1011000 => 5
0010001 => [2,1,3,1] => 1011001 => 4
0010010 => [2,1,2,1,1] => 1011011 => 2
0010011 => [2,1,2,2] => 1011010 => 5
0010100 => [2,1,1,1,2] => 1011110 => 3
0010101 => [2,1,1,1,1,1] => 1011111 => 1
0010110 => [2,1,1,2,1] => 1011101 => 3
0010111 => [2,1,1,3] => 1011100 => 4
0011000 => [2,2,3] => 1010100 => 6
0011001 => [2,2,2,1] => 1010101 => 3
0011010 => [2,2,1,1,1] => 1010111 => 2
0011011 => [2,2,1,2] => 1010110 => 4
0011100 => [2,3,2] => 1010010 => 5
0011101 => [2,3,1,1] => 1010011 => 4
0011110 => [2,4,1] => 1010001 => 5
0011111 => [2,5] => 1010000 => 6
0100000 => [1,1,5] => 1110000 => 6
0100001 => [1,1,4,1] => 1110001 => 5
0100010 => [1,1,3,1,1] => 1110011 => 4
0100011 => [1,1,3,2] => 1110010 => 6
0100100 => [1,1,2,1,2] => 1110110 => 6
0100101 => [1,1,2,1,1,1] => 1110111 => 3
0100110 => [1,1,2,2,1] => 1110101 => 5
0100111 => [1,1,2,3] => 1110100 => 6
0101000 => [1,1,1,1,3] => 1111100 => 6
0101001 => [1,1,1,1,2,1] => 1111101 => 5
0101010 => [1,1,1,1,1,1,1] => 1111111 => 0
0101011 => [1,1,1,1,1,2] => 1111110 => 6
0101100 => [1,1,1,2,2] => 1111010 => 6
0101101 => [1,1,1,2,1,1] => 1111011 => 4
0101110 => [1,1,1,3,1] => 1111001 => 5
0101111 => [1,1,1,4] => 1111000 => 6
0110000 => [1,2,4] => 1101000 => 6
0110001 => [1,2,3,1] => 1101001 => 5
0110010 => [1,2,2,1,1] => 1101011 => 4
0110011 => [1,2,2,2] => 1101010 => 6
0110100 => [1,2,1,1,2] => 1101110 => 5
0110101 => [1,2,1,1,1,1] => 1101111 => 2
0110110 => [1,2,1,2,1] => 1101101 => 4
0110111 => [1,2,1,3] => 1101100 => 6
0111000 => [1,3,3] => 1100100 => 6
0111001 => [1,3,2,1] => 1100101 => 5
0111010 => [1,3,1,1,1] => 1100111 => 3
0111011 => [1,3,1,2] => 1100110 => 5
0111100 => [1,4,2] => 1100010 => 6
0111101 => [1,4,1,1] => 1100011 => 4
0111110 => [1,5,1] => 1100001 => 5
0111111 => [1,6] => 1100000 => 6
1000000 => [1,6] => 1100000 => 6
1000001 => [1,5,1] => 1100001 => 5
1000010 => [1,4,1,1] => 1100011 => 4
1000011 => [1,4,2] => 1100010 => 6
1000100 => [1,3,1,2] => 1100110 => 5
1000101 => [1,3,1,1,1] => 1100111 => 3
1000110 => [1,3,2,1] => 1100101 => 5
1000111 => [1,3,3] => 1100100 => 6
1001000 => [1,2,1,3] => 1101100 => 6
1001001 => [1,2,1,2,1] => 1101101 => 4
1001010 => [1,2,1,1,1,1] => 1101111 => 2
1001011 => [1,2,1,1,2] => 1101110 => 5
1001100 => [1,2,2,2] => 1101010 => 6
1001101 => [1,2,2,1,1] => 1101011 => 4
1001110 => [1,2,3,1] => 1101001 => 5
1001111 => [1,2,4] => 1101000 => 6
1010000 => [1,1,1,4] => 1111000 => 6
1010001 => [1,1,1,3,1] => 1111001 => 5
1010010 => [1,1,1,2,1,1] => 1111011 => 4
1010011 => [1,1,1,2,2] => 1111010 => 6
1010100 => [1,1,1,1,1,2] => 1111110 => 6
1010101 => [1,1,1,1,1,1,1] => 1111111 => 0
1010110 => [1,1,1,1,2,1] => 1111101 => 5
1010111 => [1,1,1,1,3] => 1111100 => 6
1011000 => [1,1,2,3] => 1110100 => 6
1011001 => [1,1,2,2,1] => 1110101 => 5
1011010 => [1,1,2,1,1,1] => 1110111 => 3
1011011 => [1,1,2,1,2] => 1110110 => 6
1011100 => [1,1,3,2] => 1110010 => 6
1011101 => [1,1,3,1,1] => 1110011 => 4
1011110 => [1,1,4,1] => 1110001 => 5
1011111 => [1,1,5] => 1110000 => 6
1100000 => [2,5] => 1010000 => 6
1100001 => [2,4,1] => 1010001 => 5
1100010 => [2,3,1,1] => 1010011 => 4
1100011 => [2,3,2] => 1010010 => 5
1100100 => [2,2,1,2] => 1010110 => 4
1100101 => [2,2,1,1,1] => 1010111 => 2
1100110 => [2,2,2,1] => 1010101 => 3
1100111 => [2,2,3] => 1010100 => 6
1101000 => [2,1,1,3] => 1011100 => 4
1101001 => [2,1,1,2,1] => 1011101 => 3
1101010 => [2,1,1,1,1,1] => 1011111 => 1
1101011 => [2,1,1,1,2] => 1011110 => 3
1101100 => [2,1,2,2] => 1011010 => 5
1101101 => [2,1,2,1,1] => 1011011 => 2
1101110 => [2,1,3,1] => 1011001 => 4
1101111 => [2,1,4] => 1011000 => 5
1110000 => [3,4] => 1001000 => 6
1110001 => [3,3,1] => 1001001 => 4
1110010 => [3,2,1,1] => 1001011 => 3
1110011 => [3,2,2] => 1001010 => 4
1110100 => [3,1,1,2] => 1001110 => 3
1110101 => [3,1,1,1,1] => 1001111 => 2
1110110 => [3,1,2,1] => 1001101 => 3
1110111 => [3,1,3] => 1001100 => 5
1111000 => [4,3] => 1000100 => 5
1111001 => [4,2,1] => 1000101 => 4
1111010 => [4,1,1,1] => 1000111 => 3
1111011 => [4,1,2] => 1000110 => 4
1111100 => [5,2] => 1000010 => 5
1111101 => [5,1,1] => 1000011 => 4
1111110 => [6,1] => 1000001 => 5
1111111 => [7] => 1000000 => 6
00000000 => [8] => 10000000 => 7
00000001 => [7,1] => 10000001 => 6
00000010 => [6,1,1] => 10000011 => 5
00000011 => [6,2] => 10000010 => 6
00000100 => [5,1,2] => 10000110 => 5
00000101 => [5,1,1,1] => 10000111 => 4
00000110 => [5,2,1] => 10000101 => 5
00000111 => [5,3] => 10000100 => 6
00001000 => [4,1,3] => 10001100 => 5
00001001 => [4,1,2,1] => 10001101 => 4
00001010 => [4,1,1,1,1] => 10001111 => 3
00001011 => [4,1,1,2] => 10001110 => 4
00001100 => [4,2,2] => 10001010 => 5
00001101 => [4,2,1,1] => 10001011 => 4
00001110 => [4,3,1] => 10001001 => 5
00001111 => [4,4] => 10001000 => 3
00010000 => [3,1,4] => 10011000 => 6
00010001 => [3,1,3,1] => 10011001 => 2
00010010 => [3,1,2,1,1] => 10011011 => 3
00010011 => [3,1,2,2] => 10011010 => 4
00010100 => [3,1,1,1,2] => 10011110 => 3
00010101 => [3,1,1,1,1,1] => 10011111 => 2
00010110 => [3,1,1,2,1] => 10011101 => 3
00010111 => [3,1,1,3] => 10011100 => 5
00011000 => [3,2,3] => 10010100 => 6
00011001 => [3,2,2,1] => 10010101 => 4
00011010 => [3,2,1,1,1] => 10010111 => 3
00011011 => [3,2,1,2] => 10010110 => 4
00011100 => [3,3,2] => 10010010 => 5
00011101 => [3,3,1,1] => 10010011 => 4
00011110 => [3,4,1] => 10010001 => 6
00011111 => [3,5] => 10010000 => 7
00100000 => [2,1,5] => 10110000 => 6
00100001 => [2,1,4,1] => 10110001 => 5
00100010 => [2,1,3,1,1] => 10110011 => 4
00100011 => [2,1,3,2] => 10110010 => 6
00100100 => [2,1,2,1,2] => 10110110 => 5
00100101 => [2,1,2,1,1,1] => 10110111 => 2
00100110 => [2,1,2,2,1] => 10110101 => 4
00100111 => [2,1,2,3] => 10110100 => 6
00101000 => [2,1,1,1,3] => 10111100 => 4
00101001 => [2,1,1,1,2,1] => 10111101 => 3
00101010 => [2,1,1,1,1,1,1] => 10111111 => 1
00101011 => [2,1,1,1,1,2] => 10111110 => 3
00101100 => [2,1,1,2,2] => 10111010 => 5
00101101 => [2,1,1,2,1,1] => 10111011 => 1
00101110 => [2,1,1,3,1] => 10111001 => 4
00101111 => [2,1,1,4] => 10111000 => 5
00110000 => [2,2,4] => 10101000 => 7
00110001 => [2,2,3,1] => 10101001 => 6
00110010 => [2,2,2,1,1] => 10101011 => 3
00110011 => [2,2,2,2] => 10101010 => 1
00110100 => [2,2,1,1,2] => 10101110 => 4
00110101 => [2,2,1,1,1,1] => 10101111 => 2
00110110 => [2,2,1,2,1] => 10101101 => 3
00110111 => [2,2,1,3] => 10101100 => 5
00111000 => [2,3,3] => 10100100 => 7
00111001 => [2,3,2,1] => 10100101 => 5
00111010 => [2,3,1,1,1] => 10100111 => 4
00111011 => [2,3,1,2] => 10100110 => 5
00111100 => [2,4,2] => 10100010 => 6
00111101 => [2,4,1,1] => 10100011 => 5
00111110 => [2,5,1] => 10100001 => 6
00111111 => [2,6] => 10100000 => 7
01000000 => [1,1,6] => 11100000 => 7
01000001 => [1,1,5,1] => 11100001 => 6
01000010 => [1,1,4,1,1] => 11100011 => 5
01000011 => [1,1,4,2] => 11100010 => 7
01000100 => [1,1,3,1,2] => 11100110 => 7
01000101 => [1,1,3,1,1,1] => 11100111 => 4
01000110 => [1,1,3,2,1] => 11100101 => 6
01000111 => [1,1,3,3] => 11100100 => 7
01001000 => [1,1,2,1,3] => 11101100 => 7
01001001 => [1,1,2,1,2,1] => 11101101 => 6
01001010 => [1,1,2,1,1,1,1] => 11101111 => 3
01001011 => [1,1,2,1,1,2] => 11101110 => 3
01001100 => [1,1,2,2,2] => 11101010 => 7
01001101 => [1,1,2,2,1,1] => 11101011 => 5
01001110 => [1,1,2,3,1] => 11101001 => 6
01001111 => [1,1,2,4] => 11101000 => 7
01010000 => [1,1,1,1,4] => 11111000 => 7
01010001 => [1,1,1,1,3,1] => 11111001 => 6
01010010 => [1,1,1,1,2,1,1] => 11111011 => 5
01010011 => [1,1,1,1,2,2] => 11111010 => 7
01010100 => [1,1,1,1,1,1,2] => 11111110 => 7
01010101 => [1,1,1,1,1,1,1,1] => 11111111 => 0
01010110 => [1,1,1,1,1,2,1] => 11111101 => 6
01010111 => [1,1,1,1,1,3] => 11111100 => 7
01011000 => [1,1,1,2,3] => 11110100 => 7
01011001 => [1,1,1,2,2,1] => 11110101 => 6
01011010 => [1,1,1,2,1,1,1] => 11110111 => 4
01011011 => [1,1,1,2,1,2] => 11110110 => 7
01011100 => [1,1,1,3,2] => 11110010 => 7
01011101 => [1,1,1,3,1,1] => 11110011 => 5
01011110 => [1,1,1,4,1] => 11110001 => 6
01011111 => [1,1,1,5] => 11110000 => 7
01100000 => [1,2,5] => 11010000 => 7
01100001 => [1,2,4,1] => 11010001 => 6
01100010 => [1,2,3,1,1] => 11010011 => 5
01100011 => [1,2,3,2] => 11010010 => 7
01100100 => [1,2,2,1,2] => 11010110 => 6
01100101 => [1,2,2,1,1,1] => 11010111 => 4
01100110 => [1,2,2,2,1] => 11010101 => 6
01100111 => [1,2,2,3] => 11010100 => 7
01101000 => [1,2,1,1,3] => 11011100 => 6
01101001 => [1,2,1,1,2,1] => 11011101 => 2
01101010 => [1,2,1,1,1,1,1] => 11011111 => 2
01101011 => [1,2,1,1,1,2] => 11011110 => 5
01101100 => [1,2,1,2,2] => 11011010 => 7
01101101 => [1,2,1,2,1,1] => 11011011 => 4
01101110 => [1,2,1,3,1] => 11011001 => 6
01101111 => [1,2,1,4] => 11011000 => 7
01110000 => [1,3,4] => 11001000 => 7
01110001 => [1,3,3,1] => 11001001 => 6
01110010 => [1,3,2,1,1] => 11001011 => 5
01110011 => [1,3,2,2] => 11001010 => 7
01110100 => [1,3,1,1,2] => 11001110 => 5
01110101 => [1,3,1,1,1,1] => 11001111 => 3
01110110 => [1,3,1,2,1] => 11001101 => 5
01110111 => [1,3,1,3] => 11001100 => 3
01111000 => [1,4,3] => 11000100 => 7
01111001 => [1,4,2,1] => 11000101 => 6
01111010 => [1,4,1,1,1] => 11000111 => 4
01111011 => [1,4,1,2] => 11000110 => 6
01111100 => [1,5,2] => 11000010 => 7
01111101 => [1,5,1,1] => 11000011 => 5
01111110 => [1,6,1] => 11000001 => 6
01111111 => [1,7] => 11000000 => 7
10000000 => [1,7] => 11000000 => 7
10000001 => [1,6,1] => 11000001 => 6
10000010 => [1,5,1,1] => 11000011 => 5
10000011 => [1,5,2] => 11000010 => 7
10000100 => [1,4,1,2] => 11000110 => 6
10000101 => [1,4,1,1,1] => 11000111 => 4
10000110 => [1,4,2,1] => 11000101 => 6
10000111 => [1,4,3] => 11000100 => 7
10001000 => [1,3,1,3] => 11001100 => 3
10001001 => [1,3,1,2,1] => 11001101 => 5
10001010 => [1,3,1,1,1,1] => 11001111 => 3
10001011 => [1,3,1,1,2] => 11001110 => 5
10001100 => [1,3,2,2] => 11001010 => 7
10001101 => [1,3,2,1,1] => 11001011 => 5
10001110 => [1,3,3,1] => 11001001 => 6
10001111 => [1,3,4] => 11001000 => 7
10010000 => [1,2,1,4] => 11011000 => 7
10010001 => [1,2,1,3,1] => 11011001 => 6
10010010 => [1,2,1,2,1,1] => 11011011 => 4
10010011 => [1,2,1,2,2] => 11011010 => 7
10010100 => [1,2,1,1,1,2] => 11011110 => 5
10010101 => [1,2,1,1,1,1,1] => 11011111 => 2
10010110 => [1,2,1,1,2,1] => 11011101 => 2
10010111 => [1,2,1,1,3] => 11011100 => 6
10011000 => [1,2,2,3] => 11010100 => 7
10011001 => [1,2,2,2,1] => 11010101 => 6
10011010 => [1,2,2,1,1,1] => 11010111 => 4
10011011 => [1,2,2,1,2] => 11010110 => 6
10011100 => [1,2,3,2] => 11010010 => 7
10011101 => [1,2,3,1,1] => 11010011 => 5
10011110 => [1,2,4,1] => 11010001 => 6
10011111 => [1,2,5] => 11010000 => 7
10100000 => [1,1,1,5] => 11110000 => 7
10100001 => [1,1,1,4,1] => 11110001 => 6
10100010 => [1,1,1,3,1,1] => 11110011 => 5
10100011 => [1,1,1,3,2] => 11110010 => 7
10100100 => [1,1,1,2,1,2] => 11110110 => 7
10100101 => [1,1,1,2,1,1,1] => 11110111 => 4
10100110 => [1,1,1,2,2,1] => 11110101 => 6
10100111 => [1,1,1,2,3] => 11110100 => 7
10101000 => [1,1,1,1,1,3] => 11111100 => 7
10101001 => [1,1,1,1,1,2,1] => 11111101 => 6
10101010 => [1,1,1,1,1,1,1,1] => 11111111 => 0
10101011 => [1,1,1,1,1,1,2] => 11111110 => 7
10101100 => [1,1,1,1,2,2] => 11111010 => 7
10101101 => [1,1,1,1,2,1,1] => 11111011 => 5
10101110 => [1,1,1,1,3,1] => 11111001 => 6
10101111 => [1,1,1,1,4] => 11111000 => 7
10110000 => [1,1,2,4] => 11101000 => 7
10110001 => [1,1,2,3,1] => 11101001 => 6
10110010 => [1,1,2,2,1,1] => 11101011 => 5
10110011 => [1,1,2,2,2] => 11101010 => 7
10110100 => [1,1,2,1,1,2] => 11101110 => 3
10110101 => [1,1,2,1,1,1,1] => 11101111 => 3
10110110 => [1,1,2,1,2,1] => 11101101 => 6
10110111 => [1,1,2,1,3] => 11101100 => 7
10111000 => [1,1,3,3] => 11100100 => 7
10111001 => [1,1,3,2,1] => 11100101 => 6
10111010 => [1,1,3,1,1,1] => 11100111 => 4
10111011 => [1,1,3,1,2] => 11100110 => 7
10111100 => [1,1,4,2] => 11100010 => 7
10111101 => [1,1,4,1,1] => 11100011 => 5
10111110 => [1,1,5,1] => 11100001 => 6
10111111 => [1,1,6] => 11100000 => 7
11000000 => [2,6] => 10100000 => 7
11000001 => [2,5,1] => 10100001 => 6
11000010 => [2,4,1,1] => 10100011 => 5
11000011 => [2,4,2] => 10100010 => 6
11000100 => [2,3,1,2] => 10100110 => 5
11000101 => [2,3,1,1,1] => 10100111 => 4
11000110 => [2,3,2,1] => 10100101 => 5
11000111 => [2,3,3] => 10100100 => 7
11001000 => [2,2,1,3] => 10101100 => 5
11001001 => [2,2,1,2,1] => 10101101 => 3
11001010 => [2,2,1,1,1,1] => 10101111 => 2
11001011 => [2,2,1,1,2] => 10101110 => 4
11001100 => [2,2,2,2] => 10101010 => 1
11001101 => [2,2,2,1,1] => 10101011 => 3
11001110 => [2,2,3,1] => 10101001 => 6
11001111 => [2,2,4] => 10101000 => 7
11010000 => [2,1,1,4] => 10111000 => 5
11010001 => [2,1,1,3,1] => 10111001 => 4
11010010 => [2,1,1,2,1,1] => 10111011 => 1
11010011 => [2,1,1,2,2] => 10111010 => 5
11010100 => [2,1,1,1,1,2] => 10111110 => 3
11010101 => [2,1,1,1,1,1,1] => 10111111 => 1
11010110 => [2,1,1,1,2,1] => 10111101 => 3
11010111 => [2,1,1,1,3] => 10111100 => 4
11011000 => [2,1,2,3] => 10110100 => 6
11011001 => [2,1,2,2,1] => 10110101 => 4
11011010 => [2,1,2,1,1,1] => 10110111 => 2
11011011 => [2,1,2,1,2] => 10110110 => 5
11011100 => [2,1,3,2] => 10110010 => 6
11011101 => [2,1,3,1,1] => 10110011 => 4
11011110 => [2,1,4,1] => 10110001 => 5
11011111 => [2,1,5] => 10110000 => 6
11100000 => [3,5] => 10010000 => 7
11100001 => [3,4,1] => 10010001 => 6
11100010 => [3,3,1,1] => 10010011 => 4
11100011 => [3,3,2] => 10010010 => 5
11100100 => [3,2,1,2] => 10010110 => 4
11100101 => [3,2,1,1,1] => 10010111 => 3
11100110 => [3,2,2,1] => 10010101 => 4
11100111 => [3,2,3] => 10010100 => 6
11101000 => [3,1,1,3] => 10011100 => 5
11101001 => [3,1,1,2,1] => 10011101 => 3
11101010 => [3,1,1,1,1,1] => 10011111 => 2
11101011 => [3,1,1,1,2] => 10011110 => 3
11101100 => [3,1,2,2] => 10011010 => 4
11101101 => [3,1,2,1,1] => 10011011 => 3
11101110 => [3,1,3,1] => 10011001 => 2
11101111 => [3,1,4] => 10011000 => 6
11110000 => [4,4] => 10001000 => 3
11110001 => [4,3,1] => 10001001 => 5
11110010 => [4,2,1,1] => 10001011 => 4
11110011 => [4,2,2] => 10001010 => 5
11110100 => [4,1,1,2] => 10001110 => 4
11110101 => [4,1,1,1,1] => 10001111 => 3
11110110 => [4,1,2,1] => 10001101 => 4
11110111 => [4,1,3] => 10001100 => 5
11111000 => [5,3] => 10000100 => 6
11111001 => [5,2,1] => 10000101 => 5
11111010 => [5,1,1,1] => 10000111 => 4
11111011 => [5,1,2] => 10000110 => 5
11111100 => [6,2] => 10000010 => 6
11111101 => [6,1,1] => 10000011 => 5
11111110 => [7,1] => 10000001 => 6
11111111 => [8] => 10000000 => 7
000000000 => [9] => 100000000 => 8
000000001 => [8,1] => 100000001 => 7
000000010 => [7,1,1] => 100000011 => 6
000000011 => [7,2] => 100000010 => 7
000000100 => [6,1,2] => 100000110 => 6
000000101 => [6,1,1,1] => 100000111 => 5
000000110 => [6,2,1] => 100000101 => 6
000000111 => [6,3] => 100000100 => 7
000001000 => [5,1,3] => 100001100 => 6
000001001 => [5,1,2,1] => 100001101 => 5
000001010 => [5,1,1,1,1] => 100001111 => 4
000001011 => [5,1,1,2] => 100001110 => 5
000001100 => [5,2,2] => 100001010 => 6
000001101 => [5,2,1,1] => 100001011 => 5
000001110 => [5,3,1] => 100001001 => 6
000001111 => [5,4] => 100001000 => 7
000010000 => [4,1,4] => 100011000 => 7
000010001 => [4,1,3,1] => 100011001 => 5
000010010 => [4,1,2,1,1] => 100011011 => 4
000010011 => [4,1,2,2] => 100011010 => 5
000010100 => [4,1,1,1,2] => 100011110 => 4
000010101 => [4,1,1,1,1,1] => 100011111 => 3
000010110 => [4,1,1,2,1] => 100011101 => 4
000010111 => [4,1,1,3] => 100011100 => 5
000011000 => [4,2,3] => 100010100 => 6
000011001 => [4,2,2,1] => 100010101 => 5
000011010 => [4,2,1,1,1] => 100010111 => 4
000011011 => [4,2,1,2] => 100010110 => 5
000011100 => [4,3,2] => 100010010 => 6
000011101 => [4,3,1,1] => 100010011 => 5
000011110 => [4,4,1] => 100010001 => 6
000011111 => [4,5] => 100010000 => 8
000100000 => [3,1,5] => 100110000 => 7
000100001 => [3,1,4,1] => 100110001 => 6
000100010 => [3,1,3,1,1] => 100110011 => 4
000100011 => [3,1,3,2] => 100110010 => 6
000100100 => [3,1,2,1,2] => 100110110 => 4
000100101 => [3,1,2,1,1,1] => 100110111 => 3
000100110 => [3,1,2,2,1] => 100110101 => 4
000100111 => [3,1,2,3] => 100110100 => 6
000101000 => [3,1,1,1,3] => 100111100 => 5
000101001 => [3,1,1,1,2,1] => 100111101 => 3
000101010 => [3,1,1,1,1,1,1] => 100111111 => 2
000101011 => [3,1,1,1,1,2] => 100111110 => 3
000101100 => [3,1,1,2,2] => 100111010 => 4
000101101 => [3,1,1,2,1,1] => 100111011 => 3
000101110 => [3,1,1,3,1] => 100111001 => 5
000101111 => [3,1,1,4] => 100111000 => 6
000110000 => [3,2,4] => 100101000 => 7
000110001 => [3,2,3,1] => 100101001 => 5
000110010 => [3,2,2,1,1] => 100101011 => 4
000110011 => [3,2,2,2] => 100101010 => 5
000110100 => [3,2,1,1,2] => 100101110 => 4
000110101 => [3,2,1,1,1,1] => 100101111 => 3
000110110 => [3,2,1,2,1] => 100101101 => 4
000110111 => [3,2,1,3] => 100101100 => 6
000111000 => [3,3,3] => 100100100 => 2
000111001 => [3,3,2,1] => 100100101 => 5
000111010 => [3,3,1,1,1] => 100100111 => 4
000111011 => [3,3,1,2] => 100100110 => 5
000111100 => [3,4,2] => 100100010 => 7
000111101 => [3,4,1,1] => 100100011 => 6
000111110 => [3,5,1] => 100100001 => 7
000111111 => [3,6] => 100100000 => 8
001000000 => [2,1,6] => 101100000 => 7
001000001 => [2,1,5,1] => 101100001 => 6
001000010 => [2,1,4,1,1] => 101100011 => 5
001000011 => [2,1,4,2] => 101100010 => 7
001000100 => [2,1,3,1,2] => 101100110 => 6
001000101 => [2,1,3,1,1,1] => 101100111 => 4
001000110 => [2,1,3,2,1] => 101100101 => 5
001000111 => [2,1,3,3] => 101100100 => 7
001001000 => [2,1,2,1,3] => 101101100 => 6
001001001 => [2,1,2,1,2,1] => 101101101 => 1
001001010 => [2,1,2,1,1,1,1] => 101101111 => 2
001001011 => [2,1,2,1,1,2] => 101101110 => 4
001001100 => [2,1,2,2,2] => 101101010 => 7
001001101 => [2,1,2,2,1,1] => 101101011 => 4
001001110 => [2,1,2,3,1] => 101101001 => 6
001001111 => [2,1,2,4] => 101101000 => 7
001010000 => [2,1,1,1,4] => 101111000 => 5
001010001 => [2,1,1,1,3,1] => 101111001 => 4
001010010 => [2,1,1,1,2,1,1] => 101111011 => 3
001010011 => [2,1,1,1,2,2] => 101111010 => 5
001010100 => [2,1,1,1,1,1,2] => 101111110 => 3
001010101 => [2,1,1,1,1,1,1,1] => 101111111 => 1
001010110 => [2,1,1,1,1,2,1] => 101111101 => 3
001010111 => [2,1,1,1,1,3] => 101111100 => 4
001011000 => [2,1,1,2,3] => 101110100 => 6
001011001 => [2,1,1,2,2,1] => 101110101 => 5
001011010 => [2,1,1,2,1,1,1] => 101110111 => 2
001011011 => [2,1,1,2,1,2] => 101110110 => 5
001011100 => [2,1,1,3,2] => 101110010 => 6
001011101 => [2,1,1,3,1,1] => 101110011 => 4
001011110 => [2,1,1,4,1] => 101110001 => 5
001011111 => [2,1,1,5] => 101110000 => 6
001100000 => [2,2,5] => 101010000 => 8
001100001 => [2,2,4,1] => 101010001 => 7
001100010 => [2,2,3,1,1] => 101010011 => 6
001100011 => [2,2,3,2] => 101010010 => 7
001100100 => [2,2,2,1,2] => 101010110 => 5
001100101 => [2,2,2,1,1,1] => 101010111 => 3
001100110 => [2,2,2,2,1] => 101010101 => 4
001100111 => [2,2,2,3] => 101010100 => 8
001101000 => [2,2,1,1,3] => 101011100 => 5
001101001 => [2,2,1,1,2,1] => 101011101 => 3
001101010 => [2,2,1,1,1,1,1] => 101011111 => 2
001101011 => [2,2,1,1,1,2] => 101011110 => 4
001101100 => [2,2,1,2,2] => 101011010 => 6
001101101 => [2,2,1,2,1,1] => 101011011 => 3
001101110 => [2,2,1,3,1] => 101011001 => 5
001101111 => [2,2,1,4] => 101011000 => 6
001110000 => [2,3,4] => 101001000 => 8
001110001 => [2,3,3,1] => 101001001 => 7
001110010 => [2,3,2,1,1] => 101001011 => 5
001110011 => [2,3,2,2] => 101001010 => 6
001110100 => [2,3,1,1,2] => 101001110 => 5
001110101 => [2,3,1,1,1,1] => 101001111 => 4
001110110 => [2,3,1,2,1] => 101001101 => 5
001110111 => [2,3,1,3] => 101001100 => 7
001111000 => [2,4,3] => 101000100 => 8
001111001 => [2,4,2,1] => 101000101 => 6
001111010 => [2,4,1,1,1] => 101000111 => 5
001111011 => [2,4,1,2] => 101000110 => 6
001111100 => [2,5,2] => 101000010 => 7
001111101 => [2,5,1,1] => 101000011 => 6
001111110 => [2,6,1] => 101000001 => 7
001111111 => [2,7] => 101000000 => 8
010000000 => [1,1,7] => 111000000 => 8
010000001 => [1,1,6,1] => 111000001 => 7
010000010 => [1,1,5,1,1] => 111000011 => 6
010000011 => [1,1,5,2] => 111000010 => 8
010000100 => [1,1,4,1,2] => 111000110 => 8
010000101 => [1,1,4,1,1,1] => 111000111 => 5
010000110 => [1,1,4,2,1] => 111000101 => 7
010000111 => [1,1,4,3] => 111000100 => 8
010001000 => [1,1,3,1,3] => 111001100 => 8
010001001 => [1,1,3,1,2,1] => 111001101 => 7
010001010 => [1,1,3,1,1,1,1] => 111001111 => 4
010001011 => [1,1,3,1,1,2] => 111001110 => 7
010001100 => [1,1,3,2,2] => 111001010 => 8
010001101 => [1,1,3,2,1,1] => 111001011 => 6
010001110 => [1,1,3,3,1] => 111001001 => 7
010001111 => [1,1,3,4] => 111001000 => 8
010010000 => [1,1,2,1,4] => 111011000 => 8
010010001 => [1,1,2,1,3,1] => 111011001 => 7
010010010 => [1,1,2,1,2,1,1] => 111011011 => 6
010010011 => [1,1,2,1,2,2] => 111011010 => 8
010010100 => [1,1,2,1,1,1,2] => 111011110 => 7
010010101 => [1,1,2,1,1,1,1,1] => 111011111 => 3
010010110 => [1,1,2,1,1,2,1] => 111011101 => 6
010010111 => [1,1,2,1,1,3] => 111011100 => 8
010011000 => [1,1,2,2,3] => 111010100 => 8
010011001 => [1,1,2,2,2,1] => 111010101 => 7
010011010 => [1,1,2,2,1,1,1] => 111010111 => 5
010011011 => [1,1,2,2,1,2] => 111010110 => 8
010011100 => [1,1,2,3,2] => 111010010 => 8
010011101 => [1,1,2,3,1,1] => 111010011 => 6
010011110 => [1,1,2,4,1] => 111010001 => 7
010011111 => [1,1,2,5] => 111010000 => 8
010100000 => [1,1,1,1,5] => 111110000 => 8
010100001 => [1,1,1,1,4,1] => 111110001 => 7
010100010 => [1,1,1,1,3,1,1] => 111110011 => 6
010100011 => [1,1,1,1,3,2] => 111110010 => 8
010100100 => [1,1,1,1,2,1,2] => 111110110 => 8
010100101 => [1,1,1,1,2,1,1,1] => 111110111 => 5
010100110 => [1,1,1,1,2,2,1] => 111110101 => 7
010100111 => [1,1,1,1,2,3] => 111110100 => 8
010101000 => [1,1,1,1,1,1,3] => 111111100 => 8
010101001 => [1,1,1,1,1,1,2,1] => 111111101 => 7
010101010 => [1,1,1,1,1,1,1,1,1] => 111111111 => 0
010101011 => [1,1,1,1,1,1,1,2] => 111111110 => 8
010101100 => [1,1,1,1,1,2,2] => 111111010 => 8
010101101 => [1,1,1,1,1,2,1,1] => 111111011 => 6
010101110 => [1,1,1,1,1,3,1] => 111111001 => 7
010101111 => [1,1,1,1,1,4] => 111111000 => 8
010110000 => [1,1,1,2,4] => 111101000 => 8
010110001 => [1,1,1,2,3,1] => 111101001 => 7
010110010 => [1,1,1,2,2,1,1] => 111101011 => 6
010110011 => [1,1,1,2,2,2] => 111101010 => 8
010110100 => [1,1,1,2,1,1,2] => 111101110 => 8
010110101 => [1,1,1,2,1,1,1,1] => 111101111 => 4
010110110 => [1,1,1,2,1,2,1] => 111101101 => 7
010110111 => [1,1,1,2,1,3] => 111101100 => 8
010111000 => [1,1,1,3,3] => 111100100 => 8
010111001 => [1,1,1,3,2,1] => 111100101 => 7
010111010 => [1,1,1,3,1,1,1] => 111100111 => 5
010111011 => [1,1,1,3,1,2] => 111100110 => 8
010111100 => [1,1,1,4,2] => 111100010 => 8
010111101 => [1,1,1,4,1,1] => 111100011 => 6
010111110 => [1,1,1,5,1] => 111100001 => 7
010111111 => [1,1,1,6] => 111100000 => 8
011000000 => [1,2,6] => 110100000 => 8
011000001 => [1,2,5,1] => 110100001 => 7
011000010 => [1,2,4,1,1] => 110100011 => 6
011000011 => [1,2,4,2] => 110100010 => 8
011000100 => [1,2,3,1,2] => 110100110 => 7
011000101 => [1,2,3,1,1,1] => 110100111 => 5
011000110 => [1,2,3,2,1] => 110100101 => 7
011000111 => [1,2,3,3] => 110100100 => 8
011001000 => [1,2,2,1,3] => 110101100 => 8
011001001 => [1,2,2,1,2,1] => 110101101 => 6
011001010 => [1,2,2,1,1,1,1] => 110101111 => 4
011001011 => [1,2,2,1,1,2] => 110101110 => 6
011001100 => [1,2,2,2,2] => 110101010 => 8
011001101 => [1,2,2,2,1,1] => 110101011 => 6
011001110 => [1,2,2,3,1] => 110101001 => 7
011001111 => [1,2,2,4] => 110101000 => 8
011010000 => [1,2,1,1,4] => 110111000 => 7
011010001 => [1,2,1,1,3,1] => 110111001 => 6
011010010 => [1,2,1,1,2,1,1] => 110111011 => 4
011010011 => [1,2,1,1,2,2] => 110111010 => 7
011010100 => [1,2,1,1,1,1,2] => 110111110 => 5
011010101 => [1,2,1,1,1,1,1,1] => 110111111 => 2
011010110 => [1,2,1,1,1,2,1] => 110111101 => 5
011010111 => [1,2,1,1,1,3] => 110111100 => 6
011011000 => [1,2,1,2,3] => 110110100 => 8
011011001 => [1,2,1,2,2,1] => 110110101 => 7
011011010 => [1,2,1,2,1,1,1] => 110110111 => 4
011011011 => [1,2,1,2,1,2] => 110110110 => 2
011011100 => [1,2,1,3,2] => 110110010 => 8
011011101 => [1,2,1,3,1,1] => 110110011 => 6
011011110 => [1,2,1,4,1] => 110110001 => 7
011011111 => [1,2,1,5] => 110110000 => 8
011100000 => [1,3,5] => 110010000 => 8
011100001 => [1,3,4,1] => 110010001 => 7
011100010 => [1,3,3,1,1] => 110010011 => 6
011100011 => [1,3,3,2] => 110010010 => 8
011100100 => [1,3,2,1,2] => 110010110 => 7
011100101 => [1,3,2,1,1,1] => 110010111 => 5
011100110 => [1,3,2,2,1] => 110010101 => 7
011100111 => [1,3,2,3] => 110010100 => 8
011101000 => [1,3,1,1,3] => 110011100 => 7
011101001 => [1,3,1,1,2,1] => 110011101 => 5
011101010 => [1,3,1,1,1,1,1] => 110011111 => 3
011101011 => [1,3,1,1,1,2] => 110011110 => 5
011101100 => [1,3,1,2,2] => 110011010 => 7
011101101 => [1,3,1,2,1,1] => 110011011 => 5
011101110 => [1,3,1,3,1] => 110011001 => 6
011101111 => [1,3,1,4] => 110011000 => 8
011110000 => [1,4,4] => 110001000 => 8
011110001 => [1,4,3,1] => 110001001 => 7
011110010 => [1,4,2,1,1] => 110001011 => 6
011110011 => [1,4,2,2] => 110001010 => 8
011110100 => [1,4,1,1,2] => 110001110 => 6
011110101 => [1,4,1,1,1,1] => 110001111 => 4
011110110 => [1,4,1,2,1] => 110001101 => 6
011110111 => [1,4,1,3] => 110001100 => 7
011111000 => [1,5,3] => 110000100 => 8
011111001 => [1,5,2,1] => 110000101 => 7
011111010 => [1,5,1,1,1] => 110000111 => 5
011111011 => [1,5,1,2] => 110000110 => 7
011111100 => [1,6,2] => 110000010 => 8
011111101 => [1,6,1,1] => 110000011 => 6
011111110 => [1,7,1] => 110000001 => 7
011111111 => [1,8] => 110000000 => 8
100000000 => [1,8] => 110000000 => 8
100000001 => [1,7,1] => 110000001 => 7
100000010 => [1,6,1,1] => 110000011 => 6
100000011 => [1,6,2] => 110000010 => 8
100000100 => [1,5,1,2] => 110000110 => 7
100000101 => [1,5,1,1,1] => 110000111 => 5
100000110 => [1,5,2,1] => 110000101 => 7
100000111 => [1,5,3] => 110000100 => 8
100001000 => [1,4,1,3] => 110001100 => 7
100001001 => [1,4,1,2,1] => 110001101 => 6
100001010 => [1,4,1,1,1,1] => 110001111 => 4
100001011 => [1,4,1,1,2] => 110001110 => 6
100001100 => [1,4,2,2] => 110001010 => 8
100001101 => [1,4,2,1,1] => 110001011 => 6
100001110 => [1,4,3,1] => 110001001 => 7
100001111 => [1,4,4] => 110001000 => 8
100010000 => [1,3,1,4] => 110011000 => 8
100010001 => [1,3,1,3,1] => 110011001 => 6
100010010 => [1,3,1,2,1,1] => 110011011 => 5
100010011 => [1,3,1,2,2] => 110011010 => 7
100010100 => [1,3,1,1,1,2] => 110011110 => 5
100010101 => [1,3,1,1,1,1,1] => 110011111 => 3
100010110 => [1,3,1,1,2,1] => 110011101 => 5
100010111 => [1,3,1,1,3] => 110011100 => 7
100011000 => [1,3,2,3] => 110010100 => 8
100011001 => [1,3,2,2,1] => 110010101 => 7
100011010 => [1,3,2,1,1,1] => 110010111 => 5
100011011 => [1,3,2,1,2] => 110010110 => 7
100011100 => [1,3,3,2] => 110010010 => 8
100011101 => [1,3,3,1,1] => 110010011 => 6
100011110 => [1,3,4,1] => 110010001 => 7
100011111 => [1,3,5] => 110010000 => 8
100100000 => [1,2,1,5] => 110110000 => 8
100100001 => [1,2,1,4,1] => 110110001 => 7
100100010 => [1,2,1,3,1,1] => 110110011 => 6
100100011 => [1,2,1,3,2] => 110110010 => 8
100100100 => [1,2,1,2,1,2] => 110110110 => 2
100100101 => [1,2,1,2,1,1,1] => 110110111 => 4
100100110 => [1,2,1,2,2,1] => 110110101 => 7
100100111 => [1,2,1,2,3] => 110110100 => 8
100101000 => [1,2,1,1,1,3] => 110111100 => 6
100101001 => [1,2,1,1,1,2,1] => 110111101 => 5
100101010 => [1,2,1,1,1,1,1,1] => 110111111 => 2
100101011 => [1,2,1,1,1,1,2] => 110111110 => 5
100101100 => [1,2,1,1,2,2] => 110111010 => 7
100101101 => [1,2,1,1,2,1,1] => 110111011 => 4
100101110 => [1,2,1,1,3,1] => 110111001 => 6
100101111 => [1,2,1,1,4] => 110111000 => 7
100110000 => [1,2,2,4] => 110101000 => 8
100110001 => [1,2,2,3,1] => 110101001 => 7
100110010 => [1,2,2,2,1,1] => 110101011 => 6
100110011 => [1,2,2,2,2] => 110101010 => 8
100110100 => [1,2,2,1,1,2] => 110101110 => 6
100110101 => [1,2,2,1,1,1,1] => 110101111 => 4
100110110 => [1,2,2,1,2,1] => 110101101 => 6
100110111 => [1,2,2,1,3] => 110101100 => 8
100111000 => [1,2,3,3] => 110100100 => 8
100111001 => [1,2,3,2,1] => 110100101 => 7
100111010 => [1,2,3,1,1,1] => 110100111 => 5
100111011 => [1,2,3,1,2] => 110100110 => 7
100111100 => [1,2,4,2] => 110100010 => 8
100111101 => [1,2,4,1,1] => 110100011 => 6
100111110 => [1,2,5,1] => 110100001 => 7
100111111 => [1,2,6] => 110100000 => 8
101000000 => [1,1,1,6] => 111100000 => 8
101000001 => [1,1,1,5,1] => 111100001 => 7
101000010 => [1,1,1,4,1,1] => 111100011 => 6
101000011 => [1,1,1,4,2] => 111100010 => 8
101000100 => [1,1,1,3,1,2] => 111100110 => 8
101000101 => [1,1,1,3,1,1,1] => 111100111 => 5
101000110 => [1,1,1,3,2,1] => 111100101 => 7
101000111 => [1,1,1,3,3] => 111100100 => 8
101001000 => [1,1,1,2,1,3] => 111101100 => 8
101001001 => [1,1,1,2,1,2,1] => 111101101 => 7
101001010 => [1,1,1,2,1,1,1,1] => 111101111 => 4
101001011 => [1,1,1,2,1,1,2] => 111101110 => 8
101001100 => [1,1,1,2,2,2] => 111101010 => 8
101001101 => [1,1,1,2,2,1,1] => 111101011 => 6
101001110 => [1,1,1,2,3,1] => 111101001 => 7
101001111 => [1,1,1,2,4] => 111101000 => 8
101010000 => [1,1,1,1,1,4] => 111111000 => 8
101010001 => [1,1,1,1,1,3,1] => 111111001 => 7
101010010 => [1,1,1,1,1,2,1,1] => 111111011 => 6
101010011 => [1,1,1,1,1,2,2] => 111111010 => 8
101010100 => [1,1,1,1,1,1,1,2] => 111111110 => 8
101010101 => [1,1,1,1,1,1,1,1,1] => 111111111 => 0
101010110 => [1,1,1,1,1,1,2,1] => 111111101 => 7
101010111 => [1,1,1,1,1,1,3] => 111111100 => 8
101011000 => [1,1,1,1,2,3] => 111110100 => 8
101011001 => [1,1,1,1,2,2,1] => 111110101 => 7
101011010 => [1,1,1,1,2,1,1,1] => 111110111 => 5
101011011 => [1,1,1,1,2,1,2] => 111110110 => 8
101011100 => [1,1,1,1,3,2] => 111110010 => 8
101011101 => [1,1,1,1,3,1,1] => 111110011 => 6
101011110 => [1,1,1,1,4,1] => 111110001 => 7
101011111 => [1,1,1,1,5] => 111110000 => 8
101100000 => [1,1,2,5] => 111010000 => 8
101100001 => [1,1,2,4,1] => 111010001 => 7
101100010 => [1,1,2,3,1,1] => 111010011 => 6
101100011 => [1,1,2,3,2] => 111010010 => 8
101100100 => [1,1,2,2,1,2] => 111010110 => 8
101100101 => [1,1,2,2,1,1,1] => 111010111 => 5
101100110 => [1,1,2,2,2,1] => 111010101 => 7
101100111 => [1,1,2,2,3] => 111010100 => 8
101101000 => [1,1,2,1,1,3] => 111011100 => 8
101101001 => [1,1,2,1,1,2,1] => 111011101 => 6
101101010 => [1,1,2,1,1,1,1,1] => 111011111 => 3
101101011 => [1,1,2,1,1,1,2] => 111011110 => 7
101101100 => [1,1,2,1,2,2] => 111011010 => 8
101101101 => [1,1,2,1,2,1,1] => 111011011 => 6
101101110 => [1,1,2,1,3,1] => 111011001 => 7
101101111 => [1,1,2,1,4] => 111011000 => 8
101110000 => [1,1,3,4] => 111001000 => 8
101110001 => [1,1,3,3,1] => 111001001 => 7
101110010 => [1,1,3,2,1,1] => 111001011 => 6
101110011 => [1,1,3,2,2] => 111001010 => 8
101110100 => [1,1,3,1,1,2] => 111001110 => 7
101110101 => [1,1,3,1,1,1,1] => 111001111 => 4
101110110 => [1,1,3,1,2,1] => 111001101 => 7
101110111 => [1,1,3,1,3] => 111001100 => 8
101111000 => [1,1,4,3] => 111000100 => 8
101111001 => [1,1,4,2,1] => 111000101 => 7
101111010 => [1,1,4,1,1,1] => 111000111 => 5
101111011 => [1,1,4,1,2] => 111000110 => 8
101111100 => [1,1,5,2] => 111000010 => 8
101111101 => [1,1,5,1,1] => 111000011 => 6
101111110 => [1,1,6,1] => 111000001 => 7
101111111 => [1,1,7] => 111000000 => 8
110000000 => [2,7] => 101000000 => 8
110000001 => [2,6,1] => 101000001 => 7
110000010 => [2,5,1,1] => 101000011 => 6
110000011 => [2,5,2] => 101000010 => 7
110000100 => [2,4,1,2] => 101000110 => 6
110000101 => [2,4,1,1,1] => 101000111 => 5
110000110 => [2,4,2,1] => 101000101 => 6
110000111 => [2,4,3] => 101000100 => 8
110001000 => [2,3,1,3] => 101001100 => 7
110001001 => [2,3,1,2,1] => 101001101 => 5
110001010 => [2,3,1,1,1,1] => 101001111 => 4
110001011 => [2,3,1,1,2] => 101001110 => 5
110001100 => [2,3,2,2] => 101001010 => 6
110001101 => [2,3,2,1,1] => 101001011 => 5
110001110 => [2,3,3,1] => 101001001 => 7
110001111 => [2,3,4] => 101001000 => 8
110010000 => [2,2,1,4] => 101011000 => 6
110010001 => [2,2,1,3,1] => 101011001 => 5
110010010 => [2,2,1,2,1,1] => 101011011 => 3
110010011 => [2,2,1,2,2] => 101011010 => 6
110010100 => [2,2,1,1,1,2] => 101011110 => 4
110010101 => [2,2,1,1,1,1,1] => 101011111 => 2
110010110 => [2,2,1,1,2,1] => 101011101 => 3
110010111 => [2,2,1,1,3] => 101011100 => 5
110011000 => [2,2,2,3] => 101010100 => 8
110011001 => [2,2,2,2,1] => 101010101 => 4
110011010 => [2,2,2,1,1,1] => 101010111 => 3
110011011 => [2,2,2,1,2] => 101010110 => 5
110011100 => [2,2,3,2] => 101010010 => 7
110011101 => [2,2,3,1,1] => 101010011 => 6
110011110 => [2,2,4,1] => 101010001 => 7
110011111 => [2,2,5] => 101010000 => 8
110100000 => [2,1,1,5] => 101110000 => 6
110100001 => [2,1,1,4,1] => 101110001 => 5
110100010 => [2,1,1,3,1,1] => 101110011 => 4
110100011 => [2,1,1,3,2] => 101110010 => 6
110100100 => [2,1,1,2,1,2] => 101110110 => 5
110100101 => [2,1,1,2,1,1,1] => 101110111 => 2
110100110 => [2,1,1,2,2,1] => 101110101 => 5
110100111 => [2,1,1,2,3] => 101110100 => 6
110101000 => [2,1,1,1,1,3] => 101111100 => 4
110101001 => [2,1,1,1,1,2,1] => 101111101 => 3
110101010 => [2,1,1,1,1,1,1,1] => 101111111 => 1
110101011 => [2,1,1,1,1,1,2] => 101111110 => 3
110101100 => [2,1,1,1,2,2] => 101111010 => 5
110101101 => [2,1,1,1,2,1,1] => 101111011 => 3
110101110 => [2,1,1,1,3,1] => 101111001 => 4
110101111 => [2,1,1,1,4] => 101111000 => 5
110110000 => [2,1,2,4] => 101101000 => 7
110110001 => [2,1,2,3,1] => 101101001 => 6
110110010 => [2,1,2,2,1,1] => 101101011 => 4
110110011 => [2,1,2,2,2] => 101101010 => 7
110110100 => [2,1,2,1,1,2] => 101101110 => 4
110110101 => [2,1,2,1,1,1,1] => 101101111 => 2
110110110 => [2,1,2,1,2,1] => 101101101 => 1
110110111 => [2,1,2,1,3] => 101101100 => 6
110111000 => [2,1,3,3] => 101100100 => 7
110111001 => [2,1,3,2,1] => 101100101 => 5
110111010 => [2,1,3,1,1,1] => 101100111 => 4
110111011 => [2,1,3,1,2] => 101100110 => 6
110111100 => [2,1,4,2] => 101100010 => 7
110111101 => [2,1,4,1,1] => 101100011 => 5
110111110 => [2,1,5,1] => 101100001 => 6
110111111 => [2,1,6] => 101100000 => 7
111000000 => [3,6] => 100100000 => 8
111000001 => [3,5,1] => 100100001 => 7
111000010 => [3,4,1,1] => 100100011 => 6
111000011 => [3,4,2] => 100100010 => 7
111000100 => [3,3,1,2] => 100100110 => 5
111000101 => [3,3,1,1,1] => 100100111 => 4
111000110 => [3,3,2,1] => 100100101 => 5
111000111 => [3,3,3] => 100100100 => 2
111001000 => [3,2,1,3] => 100101100 => 6
111001001 => [3,2,1,2,1] => 100101101 => 4
111001010 => [3,2,1,1,1,1] => 100101111 => 3
111001011 => [3,2,1,1,2] => 100101110 => 4
111001100 => [3,2,2,2] => 100101010 => 5
111001101 => [3,2,2,1,1] => 100101011 => 4
111001110 => [3,2,3,1] => 100101001 => 5
111001111 => [3,2,4] => 100101000 => 7
111010000 => [3,1,1,4] => 100111000 => 6
111010001 => [3,1,1,3,1] => 100111001 => 5
111010010 => [3,1,1,2,1,1] => 100111011 => 3
111010011 => [3,1,1,2,2] => 100111010 => 4
111010100 => [3,1,1,1,1,2] => 100111110 => 3
111010101 => [3,1,1,1,1,1,1] => 100111111 => 2
111010110 => [3,1,1,1,2,1] => 100111101 => 3
111010111 => [3,1,1,1,3] => 100111100 => 5
111011000 => [3,1,2,3] => 100110100 => 6
111011001 => [3,1,2,2,1] => 100110101 => 4
111011010 => [3,1,2,1,1,1] => 100110111 => 3
111011011 => [3,1,2,1,2] => 100110110 => 4
111011100 => [3,1,3,2] => 100110010 => 6
111011101 => [3,1,3,1,1] => 100110011 => 4
111011110 => [3,1,4,1] => 100110001 => 6
111011111 => [3,1,5] => 100110000 => 7
111100000 => [4,5] => 100010000 => 8
111100001 => [4,4,1] => 100010001 => 6
111100010 => [4,3,1,1] => 100010011 => 5
111100011 => [4,3,2] => 100010010 => 6
111100100 => [4,2,1,2] => 100010110 => 5
111100101 => [4,2,1,1,1] => 100010111 => 4
111100110 => [4,2,2,1] => 100010101 => 5
111100111 => [4,2,3] => 100010100 => 6
111101000 => [4,1,1,3] => 100011100 => 5
111101001 => [4,1,1,2,1] => 100011101 => 4
111101010 => [4,1,1,1,1,1] => 100011111 => 3
111101011 => [4,1,1,1,2] => 100011110 => 4
111101100 => [4,1,2,2] => 100011010 => 5
111101101 => [4,1,2,1,1] => 100011011 => 4
111101110 => [4,1,3,1] => 100011001 => 5
111101111 => [4,1,4] => 100011000 => 7
111110000 => [5,4] => 100001000 => 7
111110001 => [5,3,1] => 100001001 => 6
111110010 => [5,2,1,1] => 100001011 => 5
111110011 => [5,2,2] => 100001010 => 6
111110100 => [5,1,1,2] => 100001110 => 5
111110101 => [5,1,1,1,1] => 100001111 => 4
111110110 => [5,1,2,1] => 100001101 => 5
111110111 => [5,1,3] => 100001100 => 6
111111000 => [6,3] => 100000100 => 7
111111001 => [6,2,1] => 100000101 => 6
111111010 => [6,1,1,1] => 100000111 => 5
111111011 => [6,1,2] => 100000110 => 6
111111100 => [7,2] => 100000010 => 7
111111101 => [7,1,1] => 100000011 => 6
111111110 => [8,1] => 100000001 => 7
111111111 => [9] => 100000000 => 8
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Description
The index of a given binary word in the lex-order among all its cyclic shifts.
Map
to binary word
Description
Return the composition as a binary word, treating ones as separators.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.